In the manufacture of bevel and hypoid gears with curved flank lines, the cutting tools utilized are primarily face mill cutters or face hob cutters, such types of cutting tools are well known in the art of gear manufacture. In face mill cutters, the cutting blades are arranged to cut in line with one another about a circle in the cutter head such that one tooth slot is formed with each plunge of the cutter and the cutter must be withdrawn and the workpiece indexed to the next tooth slot position in order to form the next tooth slot.
Face hobbing comprises cutting blades arranged about a cutter, not in line with each other, but in groups, with usually two or three cutting blades per group. In two-blade groups, such as disclosed by U.S. Pat. No. 4,575,285 to Blakesley and U.S. Pat. No. 4,525,108 to Krenzer, the blade pair comprises an inner or inside cutting blade (IB blade) and an outer or outside cutting blade (OB blade). In the three-blade group, such as disclosed by U.S. Pat. No. 3,760,476 to Kotthaus, a “bottom” cutting blade is included along with an inside and outside cutting blade.
Unlike most face milling processes, in which all cutting blades pass through the tooth slot during its formation, face hobbing comprises each successive group of cutting blades passing through respective successive tooth slots with each blade in the group forming a cut completely along the longitudinal portion of the tooth slot. The cutter and the workpiece rotate in a timed relationship with each other thereby allowing continual indexing of the workpiece and continual formation of each tooth slot of the gear. If the hobbing process is of the generating type, the appropriate generating motions are superimposed with the timed relationship rotations of the tool and workpiece. Thus, in face hobbing, a single plunge of the cutting tool results in all tooth slots of the workpiece being formed.
Cutting tools for face hobbing processes usually consist of disk-shaped cutter heads with stick-type cutting blades, made from bar stock high speed steel (HSS) or carbide, for example, which are inserted and positioned in slots formed in the cutter head so as to project from a face of the cutter head. Each cutting blade comprises a face portion oriented at a predetermined angle known as a side rake angle, a cutting edge, a cutting side (or pressure angle side) surface oriented at a predetermined side relief angle, a clearance edge, a clearance side surface oriented at a predetermined side relief angle, and a tip or top surface usually oriented at a predetermined top relief angle.
In one type of cutting blade, such as that shown in previously disclosed U.S. Pat. No. 3,760,476, the cutting edge is inclined with respect to a plane containing the cutter axis (axial plane) that is oriented rotationally to contact the cutting edge, the angle of inclination being known as the effective hook angle. The effective hook angle (regardless of the number of blades per group) is comprised of two elements, the built-in hook angle and the cutting blade hook angle. The built-in hook angle is the angle of a blade mounting slot machined into a cutter head. This is the angular orientation of the cutting blade body when mounted in the cutter head and is usually in the range of about 4° to 12°. The other hook angle is the actual front face angular orientation on the cutting blade. In face hobbing, the effective hook angle, which is the angle resulting from the built-in hook angle and the actual cutting blade front face hook angle, is preferably zero degrees (0°). The skilled artisan will also understand that in cutting blades having a side rake angle, the pressure angle of the cutting edge, or any change thereof, will also have influence on the effective hook angle.
In one type of cutting blade, usually found in the two-blade per group cutting tool comprising an inside cutting blade and an outside cutting blade (previously discussed U.S. Pat. No. 4,575,285 for example), the cutting blades are sharpened by removing stock material from the cutting side and clearance side surfaces only (hereafter “two-side ground” or “2-face ground” cutting blades). See FIG. 1(a). Thus, the front face and any wear coating materials (e.g. TiN, TiAlN, AlCrN, etc.) located on the front face are preserved during sharpening. However, in the two-side ground blade, the front face is not ground during sharpening and, therefore, there is no control of effective hook angle and less flexibility to control tooth surface geometry since the side rake angle and hook angle adjustments, obtained by grinding the front face, are not available.
In another type of cutting tools (for example U.S. Pat. No. 3,760,476 discussed above) the cutting blades are sharpened by grinding the cutting side surface, the clearance side relief surface and the front face. These cutting blades will hereafter be referred to as “three-side ground” or “3-face ground” cutting blades. See FIG. 1(b). By grinding the front face, adjustments to the side rake angle and the hook angle may be effected. Such changes may be utilized to keep the effective hook angle at 0° or to influence tooth surface geometry. However, by grinding the front face, any wear coatings located on the front face are destroyed.
For either 2-face ground or 3-face ground cutting blades, sharpening may be carried out on a cutting blade grinding machine such as that disclosed in U.S. Pat. Nos. 6,808,440 or 6,824,449, the disclosures of which are hereby incorporated by reference.
In order to utilize the full potential of 3-face ground and wear coatings on all three faces (i.e. “all-around” coated blades) a cutter head slot inclination angle of, for example, 4.42° may not be sufficient. In the case of 2-face ground blades, the front face remains untouched during the re-sharpening of only pressure angle and clearance sides of the blade. The front face of 2-face blades (FIG. 1(a)) is parallel to the blade shank and has a permanent coating. After re-sharpening, the blades are ready to be built in the cutter head.
If cutting blades are all-around coated, it is then recommended to grind the front face in addition to the side relief surfaces. The reason is the continuous buildup of coating layer on the front face if no stripping between coatings occurs. Although it is possible to strip the front face coating chemically before every re-coating, this would involve additional cost and results in degradation of the steel or carbide under the repeatedly stripped surface. In case of all-around coating on 3-face cutting blades, it is recommended to grind the front face of the blades in order to remove the previous coating while also providing the opportunity to achieve more optimal top rake and side rake angles with a different front face orientation. The “package” of 3-face grinding and all-around coating delivers tool lives which can double compared to 2-face grinding with permanent front face coating.
3-face grinding of cutting blades utilized in a cutter head with, for example, 4.42° of slot tilt angle is limited with respect to the maximal achievable top rake angle which is about zero in FIG. 2(a). If the same blade is utilized in a cutter head with a 12° slot tilt angle as shown in FIG. 2(b), the achieved top rake angle would then be 7.58°. This freedom allows, for most cases of different gear geometries and cutting kinematics, the possibility to achieve a positive top rake angle.
Another important factor is the relationship between slot inclination angle and number of resharpenings. In order to accomplish an effective top rake angle of e.g. 2°, a blade built in a cutter head with a 4.42° slot inclination requires a Δy (see FIG. 2(a) or 2(b)) for the blade grinding of 2.42°. The cleanup amount of As normal to the surface will require a large blade top down ΔI1 as shown in FIG. 3(a). If a top rake angle of 2° in the cutting process should be realized in a cutter with 12° slot tilt angle, then the blade hook angle in blade grinding will be 10°, as shown in FIG. 3(b). The relationship between top down ΔI2 and front face clean up Δs is becoming more favorable by increasing the slot inclination angle. The number of re-sharpening for 3-face grinding in case of a 12° cutter slot tilt angle is about 2.7 times higher than that of a 4.42° cutter slot tilt angle.
The limits for the highest realistic slot inclination angles in cutter heads are given by the cutter design and manufacturing, as well as the higher tendency of the cutting forces to push the blades axially into the slots during the cutting process.
Two of the most important input parameters of blade geometry determination, after the pressure angle, are the effective side rake angle which indicates the “sharpness” of the blade and the effective cutting edge hook angle which indirectly defines the top rake angle. For a good cutting performance and for a good tool life, the effective cutting edge hook angle is the most important parameter. Because top rake angle and effective cutting edge hook angle are connected, it is preferable to define a 3-face blade geometry which achieves the desired effective cutting edge hook angle. In those certain cases where this is not possible due to geometry limitations, the closest possible value is usually utilized as the result.
In order to obtain the effective angles, the relationship between the cutting velocity vector (FIG. 4) and the blade coordinate system in FIG. 1(b) has to be considered. In the face hobbing cutter head of FIG. 4, the cutting plane is drawn in front of one outside blade. The reference point of the outside blade lies in the cutting plane. The angular orientation of the cutting plane is defined by the relative cutting velocity vector (between work gear and cutter rotation). The cutting velocity vector is oriented normal to the cutting plane.
The blade side rake angle shown in FIG. 1(b) is equal to the effective side rake angle, if the indicated cutting direction is equal to the X-axis of the blade coordinate system. The effective cutting edge hook angle (versus the blade hook angle) is shown in FIG. 5 which shows a three-dimensional view of the side of an inside blade. The cutting plane is indicated and contains the blade reference point. Between cutting plane and cutting edge, the effective cutting edge hook angle is indicated. The blade hook angle is shown between the extension of the front blade shank plane and a line which originates in the blade tip and has a neutral pressure angle of 0° (line X). The top rake angle, which is the angle that makes the blade tip appear sharp in the cutting process, is drawn between line X and the cutting plane.
Each material removal from the blade front will change the cutting velocity vector direction in FIG. 1(b) and FIG. 4 and therefore will also change the orientation of the cutting plane. This will in turn change the effective side rake angle as well as the effective cutting edge hook angle. If a particular effective side rake angle is chosen, then the blade related side rake angle target has to be reduced or increased depending on the relationship between the cutting velocity vector and the X-axis of the blade coordinate system. This still would not deliver the desired kinematic side rake angle in one calculation step because each change of the blade side rake angle will require a different front clean-up amount, which in turn changes the offset of the calculation point on the blade and, therefore, also changes the relative cutting velocity vector direction. A complete front clean-up is shown in FIG. 6(a) and a partial, but sufficient, front clean-up is shown in FIG. 6(b).
Because the amount of front clean-up depends on the chosen side rake angle and cutting edge hook angle, the physical blade offset will change which also changes the cutting velocity vector direction relative to the blade. Because of the cross influences between three parameters which are present in the solution formulae, a closed analytic solution of the 3-face blade geometry is not practical. In order to achieve a sufficient front clean-up and realize the effective input values, three imbedded iterations are required. The problem with imbedded iterations is the ability to achieve a stable and convergent behavior of the calculations while keeping the iterations fast. This goal is not achieved in the state of the art solutions which are available today.
The initial gear design utilizes either a theoretical blade, or a standard 2-face blade design. The final 3-face blade is based on a blade positioning in a real cutter head and is also based on a different front face geometry of outside and inside blades (see FIG. 7). The front face of the left blade is ground just enough so as to provide a front face clean-up down to the face of the cutter head. The right side blade is ground further back in the horizontal direction which results in a linear blade spacing of Sx, which is larger than the spacing S of the reference cutter which is the theoretical value of 360° divided by twice the number of blade groups. This large grind-back of the right side blade will influence the tooth thickness of the manufactured bevel pinion or bevel gear.
FIG. 8 explains how a blade spacing error of Fd causes, in face hobbing, a radial error of Ne. In other words, the deviation from equal spacing, caused by a physically given cutter head and the 3-face blade geometry of outside and inside blades results in a tooth thickness error of the produced bevel gears. For face hobbing blades, each of the inside and outside cutting edge locations are therefore radially corrected with an amount of ΔRw=Ne/2 (with alternating signs for the inside and outside cutting blades).
Although the radial compensation of the 3-face blade will re-establish the tooth thickness, there will be some side effects. The alteration of the bade point radii compared to the calculated values causes a major side effect, namely a length crowning error on both flanks as shown in FIG. 9(a). The second 3-face blade side effect relates to the change of the effective cutting edge hook angle versus the initial 2-face value (or theoretical blade definition) which results in a flank twist as shown in FIG. 9(b). The flank twist can be eliminated by matching the effective cutting edge hook angle of the 3-face blade with the effective cutting edge hook angle of the 2-face reference blade.
The 3-face blade calculation applies the strategy of establishing the required cutter radii at the calculation point and defining side rake and top rake angles correctly with respect to the relative cutting direction given by the kinematic blade offset angle. While providing the requested blade geometry, the calculation has to assure a sufficient front face cleanup which has an influence on the resulting timing angle between the outside blade and the following inside blade. The initial timing angle φ of FIG. 10(a) is derived from the original 2-face calculation which is always exactly or close to 360° divided by twice the number of blade groups (which is the slot spacing angle of the cutter head). This original (i.e. initial) timing angle φ (also known as the blade spacing angle) in connection with the blade point radii of the 2-face calculation assures the cutting of the correct tooth thickness.
Three-face ground blades result in a spacing angle φx as shown in FIG. 10(b), which, according to FIG. 8, will lead to a tooth thickness error Ne. If the correct tooth thickness is re-established with small cutter point radius changes, then a length crowning side effect will occur on gears cut with such a cutter which cannot be corrected (without alterations of the machine settings).